mhd.h File Reference

Functions related to temperature and pressure used across many MHD apps. More...

#include "apps/mhd/imhd/imhd.h"

Go to the source code of this file.

Detailed Description

Functions related to temperature and pressure used across many MHD apps.

Functions
real	get_p (real gas_gamma, real rho, real E, real V2, real B2)
	Calculate pressure from MHD total energy.
real	get_E (real gas_gamma, real rho, real p, real V2, real B2)
	Calculate MHD total energy density.
void	calculate_grad_pressure (const real *q, const real *aux, real *grad_pressure, const real gas_gamma, const real rho_min=std::numeric_limits< real >::epsilon())
real	get_temperature (real p, real rho, real Ai, real Zi)
void	calculate_grad_T (const real *q, const real *aux, real *grad_T, const real gas_gamma, const real Ai=1.0, const real Zi=1.0, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
void	ensure_floor_density (const real *q, real num_q, real density_floor, real *mod_q)
void	ensure_floor_pressure (const real *q, real num_q, real gas_gamma, real pressure_floor, real *mod_q)
real	getRhoFloored (const real *q, const real rho_min=std::numeric_limits< real >::epsilon())
	Get the floored mass density.
real	getPressureFloored (const real *q, const real gas_gamma, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Get the pressure from MHD variables using floors for pressure and density.
real	getTemperatureFloored (const real *q, const real gas_gamma, const real Ai=1.0, const real Zi=1.0, const real rho_min=std::numeric_limits< real >::epsilon(), const real press_min=std::numeric_limits< real >::epsilon())
	Get the temperature from MHD variables using floors for pressure and density.

Function Documentation

calculate_grad_pressure()

void calculate_grad_pressure	(	const real *	q,
		const real *	aux,
		real *	grad_pressure,
		const real	gas_gamma,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

calculate_grad_T()

void calculate_grad_T	(	const real *	q,
		const real *	aux,
		real *	grad_T,
		const real	gas_gamma,
		const real	Ai = 1.0,
		const real	Zi = 1.0,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

ensure_floor_density()

void ensure_floor_density	(	const real *	q,
		real	num_q,
		real	density_floor,
		real *	mod_q
	)

ensure_floor_pressure()

void ensure_floor_pressure	(	const real *	q,
		real	num_q,
		real	gas_gamma,
		real	pressure_floor,
		real *	mod_q
	)

get_E()

real get_E	(	real	gas_gamma,
		real	rho,
		real	p,
		real	V2,
		real	B2
	)

Calculate MHD total energy density.

\[ e = \frac{p}{\gamma - 1} + \frac{1}{2} \rho v^2 + \frac{1}{2} B^2 \]

Parameters

gas_gamma	Ratio of specfic heats.
rho	Normalized mass density.
p	Normalized pressure.
V2	Normalized velocity squared.
B2	Normalized magnetic field squared.

Returns

Noramalized MHD energy density

get_p()

real get_p	(	real	gas_gamma,
		real	rho,
		real	E,
		real	V2,
		real	B2
	)

Calculate pressure from MHD total energy.

\[ p = (\gamma - 1) \left( e - \frac{1}{2} \rho v^2 - \frac{1}{2} B^2 \right) \]

Parameters

gas_gamma	Ratio of specfic heats.
rho	Normalized mass density.
E	MHD total energy density \(e = \frac{p}{\gamma - 1} + \frac{1}{2} \rho v^2 + \frac{1}{2} B^2 \).
V2	Normalized velocity squared.
B2	Normalized magnetic field squared.

Returns

Noramalized MHD energy density

get_temperature()

real get_temperature	(	real	p,
		real	rho,
		real	Ai,
		real	Zi
	)

getPressureFloored()

real getPressureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Get the pressure from MHD variables using floors for pressure and density.

The floored pressure is given as

\[ p_{fl} = \max(p, p_{min}), \]

where

\[ p = (\gamma - 1) \left( e - \frac{1}{2} \max(\rho, \rho_{min}) v^2 - \frac{1}{2} B^2 \right) \]

Assumes \( \rho_{min}, \; p_{min} > 0 \).

Parameters

q	The raw MHD variables.
gas_gamma	Ratio of specific heats.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

Returns

Pressure calculated assuming pressure and density floors.

getRhoFloored()

real getRhoFloored	(	const real *	q,
		const real	rho_min = std::numeric_limits< real >::epsilon()
	)

Get the floored mass density.

The floored mass density is given as

\[ \rho_{fl} = \max(\rho, \rho_{min}), \]

Assumes \( \rho_{min} > 0 \).

Parameters

q	The raw MHD variables.
rho_min	Normalized minimum mass density.

Returns

Floored mass density.

getTemperatureFloored()

real getTemperatureFloored	(	const real *	q,
		const real	gas_gamma,
		const real	Ai = 1.0,
		const real	Zi = 1.0,
		const real	rho_min = std::numeric_limits< real >::epsilon(),
		const real	press_min = std::numeric_limits< real >::epsilon()
	)

Get the temperature from MHD variables using floors for pressure and density.

Temperature is calculated assuming:

1. ideal gas: \( p = n_i T_i + n_e T_e \)
2. quasineutrality: \( Z_i n_i + Z_e n_e = 0 \)
3. electron charge: \( Z_e = -1 \)
4. temperature equilabration: \( T = T_i = T_e \)
5. MHD mass density: \( \rho_{mhd} \approx \rho_i = A_i * n_i \)

Therefore

\[ T = \frac{p_{fl}}{\rho_{fl}} \frac{ A_i } {(1 + Z_i)} \]

where

\[ p_{fl} = \max(p, p_{min}), \quad \text{and} \quad \rho_{fl} = \max(\rho, \rho_{min}). \]

Assumes \( \rho_{min}, \; p_{min} > 0 \).

Parameters

q	The raw MHD variables.
gas_gamma	Ratio of specific heats.
Ai	Proton normalized ion mass.
Zi	Ion charge.
rho_min	Normalized minimum mass density.
press_min	Normalized minimum mass density.

Returns

Temperature calculated assuming pressure and density floors.